x+(1/4x)+3=300

Solution for x+(1/4x)+3=300 equation:

x+(1/4x)+3=300

We move all terms to the left:

x+(1/4x)+3-(300)=0


Domain of the equation: 4x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

x+(+1/4x)+3-300=0

We add all the numbers together, and all the variables

x+(+1/4x)-297=0

We get rid of parentheses

x+1/4x-297=0

We multiply all the terms by the denominator


x*4x-297*4x+1=0

Wy multiply elements

4x^2-1188x+1=0

a = 4; b = -1188; c = +1;
Δ = b2-4ac
Δ = -11882-4·4·1
Δ = 1411328
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{1411328}=\sqrt{256*5513}=\sqrt{256}*\sqrt{5513}=16\sqrt{5513}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1188)-16\sqrt{5513}}{2*4}=\frac{1188-16\sqrt{5513}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1188)+16\sqrt{5513}}{2*4}=\frac{1188+16\sqrt{5513}}{8}
$